## June 2007, Game 1, Question 5

### Transcript

Question five is another global question, another must be true question. What must be true about any particular code. By this late in the game, we have a lot of previous work so we can use that for eliminations. So proceed to answer choice A. There's only one digit between the zero and the one.

Well, we've seen the zero on the one next to each other in questions three and the sketch we just did for question four, so that doesn't have to be true. There doesn't have to be exactly one digit between the zero and the one. Answer choice B says there's exactly one digit between the one in the two. And that doesn't have to be true either, if you look back to the sketch for question three.

We have the one and the two right next to each other, so there's no digit between them. Now, if you look at the next three answer choices, they're all asking about there being at most two digits between two particular numbers. So answer choice C says there are at most two digits between the one and the three. So if you wanna see if this must be true, consider have you ever put more than two digits between the one in the three?

Or was it ever possible to put more than two digits between the one of the three? So if you look at the master diagram up top, you can see that you can place the one in the first place, and you could put the three at the end that's acceptable according to that sketch. So C, isn't the answer. D says there's at most two digits between the two and the three.

Again, if you look at your sketch this time the second diagram, it's possible to put the two up front and put the three at the end. So that also doesn't have to be true, which means by default, the answer is answer choice E. And we don't need to know why it must be true because if the other four don't have to be true, this is our answer.

But if you'd like to know, there are most two digits between the two and the four. Well consider each of the parts of our master sketch in the top part of the master diagram. The two is in the second spot, so there's no way to put the four, three spaces away from the two. At best, you could put it at the very end and then there would only be two spaces between them.

So the top sketch follows the rule that there are at most two digits between the two and the 4.four. In the bottom scenario, the two in the four right next to each other. So yeah, there are no more than two spaces between them cuz in that scenario there are no spaces. So if in each of the scenario you can't put more than two spaces that means that it is true there must be at most two digits between the two and the four.

And that is it, the game is done. We move on to our next game.